Timeline for A property of subspaces of a topological space
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Aug 26, 2018 at 16:30 | comment | added | D.S. Lipham | In my previous comment, $C$ was meant to be the component $\{0\}\times [0,1]$. | |
| Aug 25, 2018 at 0:10 | comment | added | D.S. Lipham | Your remark about dense subsets is incorrect. Consider the space $X=(\{0\}\times [0,1])\cup \bigcup \{\{1/n\}\times [0,1]:n=1,2,3,...\}$. Let $A=\{\langle 0,0\rangle,\langle 0,1\rangle \} \bigcup \{\{1/n\}\times (\mathbb Q\cap [0,1]):n=1,2,3,...\}$. Define $f:X\to \mathbb R$ by $f(\langle x,y\rangle)=y$. Then $A$ is dense in $X$, $f[A\cap C]\subseteq \{0,1\}$, but $f$ is not constant on $A\cap C$. | |
| Aug 23, 2018 at 18:25 | vote | accept | Brouce | ||
| Aug 24, 2018 at 0:27 | |||||
| Aug 23, 2018 at 17:36 | comment | added | LSpice | Incidentally, there is no need for the disjunction in your statement: if $A \cap C = \emptyset$, then the condition on continuous functions is automatically satisfied. | |
| Aug 23, 2018 at 15:18 | history | edited | LSpice | CC BY-SA 4.0 |
Quantifier; named the function; \in -> \subseteq
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| Aug 23, 2018 at 14:27 | history | edited | Brouce | CC BY-SA 4.0 |
added 13 characters in body
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| Aug 23, 2018 at 12:30 | history | edited | Todd Trimble |
removed poor tag choices
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| Aug 23, 2018 at 12:11 | history | edited | Brouce | CC BY-SA 4.0 |
added 26 characters in body
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| Aug 23, 2018 at 11:50 | history | edited | Todd Trimble | CC BY-SA 4.0 |
tried to improve English
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| Aug 23, 2018 at 8:28 | history | edited | Brouce | CC BY-SA 4.0 |
edited body
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| Aug 23, 2018 at 7:19 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
typo in the title
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| Aug 23, 2018 at 5:55 | review | First posts | |||
| Aug 23, 2018 at 6:45 | |||||
| Aug 23, 2018 at 5:52 | history | asked | Brouce | CC BY-SA 4.0 |